Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Analytic perturbation of the Taylor spectrum
HTML articles powered by AMS MathViewer

by Zbigniew Slodkowski PDF
Trans. Amer. Math. Soc. 297 (1986), 319-336 Request permission

Abstract:

Let ${T_1}(z), \ldots ,{T_m}(z)$, $z \in G \subset {{\mathbf {C}}^k}$, be analytic families of bounded operators in a complex Banach space $X$, such that for each $z \in G$ the operators ${T_i}(z)$ and ${T_j}(z)$, $i,j = 1, \ldots ,n$, commute. Main result: If $K(z)$ denotes the Taylor spectrum of the tuple $({T_1}(z), \ldots ,{T_m}(z))$, then the set-valued function $K:G \to {2^{{\mathbf {C}}m}}$ is analytic. Analyticity of such set-valued functions is defined here by a simultaneous local maximum property of $k$-tuples of complex polynomials on the graph of $K$.
References
Similar Articles
Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 297 (1986), 319-336
  • MSC: Primary 47A56; Secondary 32A99, 47A10, 47D99
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0849482-9
  • MathSciNet review: 849482